The Floquet–Bloch–Gelfand transform (the FBG-transform in short), see
[1]}, [2]}, [3]}, [4]}, [5]},
\(\begin{array}{c}\displaystyle u^\varepsilon (x)\,\,\mapsto \,\,U^\varepsilon (x;\eta )=\frac{1}{\sqrt{2\pi }}\,\sum \limits _{p\in {\mathbb {Z}}}e^{-ip\eta }u^\varepsilon (x_1+p,x_2)\end{array}\) 
